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07_SEM_Chap5text - 2nd 1 Step Input order G(s A sudden...

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Dynamic Behavior: 1 st + 2 nd order G(s) In analyzing process dynamic and process control systems, it is important to know how the process responds to changes in the r 5 important to know how the process responds to changes in the process inputs . A number of standard types of input changes are widely used for hapte A number of standard types of input changes are widely used for two reasons: Ch 1. They are representative of the types of changes that occur in real operating processes. 2. They are easy to analyze mathematically. 1 1. Step Input A sudden change in a process variable can be approximated by a step change of magnitude, M : 1 st d r 5 0 0 (5-4) 0 s t U M t < ± -order response hapte The step change occurs at an arbitrary time denoted as t = 0. Ch Special Case: If M = 1, we have a “ unit step change”. We give it the symbol, S ( t ). The step change occurs at an arbitrary time denoted as 0. give it the symbol, Example of a step change: A reactor feedstock is suddenly switched from one supply to another, causing sudden 2 changes in feed concentration, flow, etc. Example: The heat input to the stirred-tank heating system in Chapter 2 is The heat input to the stirred tank heating system in Chapter 2 is suddenly changed from 8000 to 10,000 kcal/hr by changing the electrical signal to the heater. Thus, r 5 ( ) ( ) ( ) ( ) ( ) 8000 2000 , unit step , 8000 kcal/h 2 r 000 Q Q t t S t S t Q Q S Q t = + = = = ± and hapte 2 Ramp Input Ch 2. Ramp Input Industrial processes often experience “drifting disturbances”, that is, relatively slow changes up or down for some period of time. The rate of change is approximately constant. The deviation variable is U R (t) 3 is (t). We can approximate a drifting disturbance by a ramp input: ( ) 0 0 (5-7) R t U t < ± 1 st -order response r 5 0 t t a i Examples of ramp changes: hapte 1. Ramp a setpoint to a new value. (Why not make a step change?) Ch 2. Feed composition, heat exchanger fouling, catalyst activity, ambient temperature. 3. Rectangular Pulse Input It represents a brief sudden change in a process variable: 4 It represents a brief, sudden change in a process variable:
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0 for 0 t < ( ) for 0 (5-9) 0 for RP w w h t U t t t t < ± r 5 h X RP hapte 0 t w Time, t Ch E l Examples: 1. Reactor feed is shut off for one hour.
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